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We establish a bijection between $d$-simple-minded systems ($d$-SMSs) of$(-d)$-Calabi-Yau cluster category ${\cal C_{-d}}(H)$ and silting objects of${\cal D^{\rm b}}(H)$ contained in $\cal D^{\le 0}\cap \cal D^{\ge 1-d}$ forhereditary algebra $H$ of Dynkin type and $d\ge 1$. We show that the number of$d$-SMSs in ${\cal C_{-d}}(H)$ is the positive Fuss-Catalan number$C_{d}^{+}(W)$ of the corresponding Weyl group $W$, by applying this bijectionand Buan-Reiten-Thomas' and Zhu's results on Fomin-Reading's generalizedcluster complexes. Our results are based on a refined version ofsilting-$t$-structure correspondence.

Positive Fuss-Catalan numbers and Simple-minded systems in negative Calabi-Yau categories